Asteroseismic properties of solar-type stars observed with the NASA K2 mission: results from Campaigns 1-3 and prospects for future observations

We present an asteroseismic analysis of 33 solar-type stars observed in short cadence during Campaigns (C) 1-3 of the NASA K2 mission. We were able to extract both average seismic parameters and individual mode frequencies for stars with dominant frequencies up to ~3300{\mu}Hz, and we find that data for some targets are good enough to allow for a measurement of the rotational splitting. Modelling of the extracted parameters is performed by using grid-based methods using average parameters and individual frequencies together with spectroscopic parameters. For the target selection in C3, stars were chosen as in C1 and C2 to cover a wide range in parameter space to better understand the performance and noise characteristics. For C3 we still detected oscillations in 73% of the observed stars that we proposed. Future K2 campaigns hold great promise for the study of nearby clusters and the chemical evolution and age-metallicity relation of nearby field stars in the solar neighbourhood. We expect oscillations to be detected in ~388 short-cadence targets if the K2 mission continues until C18, which will greatly complement the ~500 detections of solar-like oscillations made for short-cadence targets during the nominal Kepler mission. For ~30-40 of these, including several members of the Hyades open cluster, we furthermore expect that inference from interferometry should be possible.